针对近端剂量反应函数的去偏推断

中文摘要 AI 辅助

本文利用处理变量和结果变量的混杂近端代理变量，研究存在未测量混杂时连续处理的因果剂量反应曲线的非参数推断。为估计该曲线，我们提出一种新型近端双重鲁棒伪结果，只要任意一个桥函数设定正确，其给定处理的条件均值就等于剂量反应曲线，从而填补了连续处理近端因果推断的关键空白。此外，我们推导了其平滑因果估计量的影响函数，构建了带有适当局部二次偏差校正的交叉拟合去偏局部线性估计量。我们建立了逐点和有限维渐近正态性，以及在紧凑处理区间上的均匀高斯近似。两个平滑带宽均可具有均方误差最优阶，无需欠平滑；交叉拟合则在乘积收敛速率条件下可适配灵活的桥估计量，无需拟合类熵限制。我们还开发了实用的带宽选择器、逐点置信区间和同时置信带。大量模拟和数据分析凸显了所提方法在潜在混杂和多个代理变量下的实际性能。

英文摘要

We study nonparametric inference for a continuous-treatment causal dose-response curve and its first derivative under unmeasured confounding, using treatment- and outcome-inducing proxies. We establish a proximal doubly robust pseudo-outcome whose conditional mean given treatment equals the dose-response curve whenever either bridge function is correctly specified. Their (smoothed) efficient influence function representations lead to cross-fitted local-polynomial estimators with explicit smoothing-bias correction. We establish pointwise and finite-dimensional asymptotic normality and oracle uniform Gaussian approximations over compact interior treatment intervals, allowing mean-squared-error-optimal bandwidths without undersmoothing. The derivative inference reuses the estimated bridges and the same form of bandwidth-dependent nuisance-rate conditions, evaluated at the bandwidth rate appropriate for derivative estimation, without requiring derivative-specific bridge estimation. Employing cross-fitting accommodates flexible bridge estimators under product convergence rate conditions without entropy restrictions. We further develop tests against fixed-dimensional parametric dose-response null hypotheses, including constancy, linearity, and quadratic specifications, and derive their limiting distributions under the null and local alternatives, together with practical bootstrap procedures. We also develop practical bandwidth selectors, pointwise confidence intervals, and simultaneous confidence bands for each causal estimand. Extensive simulations and a data analysis, presented in the appendix, demonstrate the finite-sample performance of the proposed methods under latent confounding and multiple proxies.

发表机构

• University of Texas at San Antonio（德克萨斯大学圣安东尼奥分校）
• Zhejiang University（浙江大学）

机构由 AI 辅助整理，请以论文原文为准。